Lauren Clayden, 21, was described by a sheriff as “heavily over the limit” after the crash, which occurred when the 11-year-old pedalled into the path of her Fiat 500.
She hit her head on the wing mirror, and was thrown into the air. She was later found to have loss of hearing in one ear.
Clayden, a geography student at Newcastle University, had been drinking with friends into the early hours of 28 June this year, and “miscalculated” that she was able to drive.
Stirling Sheriff Court was told the accident occurred at about 11am on a Saturday morning.
Clayden gave a breath sample that proved to contain 63 microgrammes of alcohol in every 100 millilitres – 1.8 times the legal limit of 35.
Prosecutor Lindsey Brooks said the accident took place on Drip Road, Stirling.
The girl, who cannot be named for legal reasons, was thought to have been initially standing over her bike on ground near the Back o’Hill Tavern, but then mounted and rode into the road. Ms Brooks said: “As the accused’s vehicle drove towards her she was seen to cycle off the side of the pavement, colliding with the accused’s vehicle.”
The child, who was not wearing a cycle helmet, was caught by the wing mirror and thrown into the air, and hit her head on the side of Clayden’s car.
Eyewitnesses called an ambulance, and waited with the child, who was bleeding from a serious head injury, until paramedics arrived.
She was taken to the Forth Valley Royal Hospital in Larbert, Stirlingshire, where she was found to have a skull fracture.
Ms Brooks said: “The accused identified herself as the driver to police at the scene. She was very upset, and said to the police that the girl had cycled right in front of her.
“Once the girl had been removed to hospital, the accused was taken to the police vehicle and the usual procedures were carried out.”
Clayden, of The Cottage, Blaircessnock Farm, Port of Menteith, Perthshire, pleaded guilty to drink driving.
Her plea of not guilty to careless driving, resulting in serious injury, was accepted by the prosecution.
Ms Brooks said: “Somebody travelling behind the accused said she had been driving in a reasonable manner, within the speed limit.
“Other witnesses also said this, and described the girl on the bike as going out in front of the accused, and the accused not having any opportunity to stop.”
The depute fiscal said the prosecution had carried out “extensive inquiries” before accepting Clayden’s plea.
Defence agent Stephen Maguire said Clayden had been “very distressed” by what had happened to the girl.
Even though, he said, there was nothing she could have done to avoid the accident, her decision to drive that morning had been “a very significant miscalculation on her part”.
He said: “Miss Clayden had been out with friends, and it was a case of the morning after the night before.
“It sounds quite harsh to say that what happened to the girl is irrelevant, but that is the legal situation.
“The whole court process has been difficult for Miss Clayden.”
Sheriff Kenneth McGowan banned Clayden from driving for 12 months, and fined her £500.
He also referred her to the drink drivers’ rehabilitation scheme, which, if completed successfully, will reduce her period of disqualification by three months.